The kernel of the quadratic form \(q(\gamma )\)  is given by dimensions vectors \((n,n,n)\) , but we have assumed that \(\gamma \)  was not of this form. One has \(q(\gamma )=1\)  only for \(\gamma =(n+1,n,n)\)  and circular permutations thereof, but the inequality is strict in the second line of (REF ) unless \(n=0\) . Hence, \(\gamma \)  must be \((1,0,0)\) , \((0,1,0)\) , or \((0,0,1)\) , with attractor invariants equal to 1. The DT invariants for \(\gamma =(n,n,n)\)  are independent of the stability conditions, and given by
the shifted Poincaré polynomial
\((-y)^{-3} P(K_{{P}^2},y)=-y^3-y-1/y\)  by [1]}.
\(\Box \)
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